WORST_CASE(?, O(n^1))

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    eval_easy2_start(Ar_0, Ar_1) -> Com_1(eval_easy2_bb0_in(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy2_bb0_in(Ar_0, Ar_1) -> Com_1(eval_easy2_0(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy2_0(Ar_0, Ar_1) -> Com_1(eval_easy2_1(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy2_1(Ar_0, Ar_1) -> Com_1(eval_easy2_2(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy2_2(Ar_0, Ar_1) -> Com_1(eval_easy2_3(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy2_3(Ar_0, Ar_1) -> Com_1(eval_easy2_4(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy2_4(Ar_0, Ar_1) -> Com_1(eval_easy2_5(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy2_5(Ar_0, Ar_1) -> Com_1(eval_easy2_6(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy2_6(Ar_0, Ar_1) -> Com_1(eval_easy2_bb1_in(Ar_1, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy2_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy2_bb2_in(Ar_0, Ar_1)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    eval_easy2_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy2_bb3_in(Ar_0, Ar_1)) [ Ar_0 <= 0 ]
		(Comp: ?, Cost: 1)    eval_easy2_bb2_in(Ar_0, Ar_1) -> Com_1(eval_easy2_bb1_in(Ar_0 - 1, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy2_bb3_in(Ar_0, Ar_1) -> Com_1(eval_easy2_stop(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(eval_easy2_start(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 1 produces the following problem:
2:	T:
		(Comp: 1, Cost: 1)    eval_easy2_start(Ar_0, Ar_1) -> Com_1(eval_easy2_bb0_in(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_bb0_in(Ar_0, Ar_1) -> Com_1(eval_easy2_0(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_0(Ar_0, Ar_1) -> Com_1(eval_easy2_1(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_1(Ar_0, Ar_1) -> Com_1(eval_easy2_2(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_2(Ar_0, Ar_1) -> Com_1(eval_easy2_3(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_3(Ar_0, Ar_1) -> Com_1(eval_easy2_4(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_4(Ar_0, Ar_1) -> Com_1(eval_easy2_5(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_5(Ar_0, Ar_1) -> Com_1(eval_easy2_6(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_6(Ar_0, Ar_1) -> Com_1(eval_easy2_bb1_in(Ar_1, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy2_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy2_bb2_in(Ar_0, Ar_1)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    eval_easy2_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy2_bb3_in(Ar_0, Ar_1)) [ Ar_0 <= 0 ]
		(Comp: ?, Cost: 1)    eval_easy2_bb2_in(Ar_0, Ar_1) -> Com_1(eval_easy2_bb1_in(Ar_0 - 1, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy2_bb3_in(Ar_0, Ar_1) -> Com_1(eval_easy2_stop(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(eval_easy2_start(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(eval_easy2_start) = 1
	Pol(eval_easy2_bb0_in) = 1
	Pol(eval_easy2_0) = 1
	Pol(eval_easy2_1) = 1
	Pol(eval_easy2_2) = 1
	Pol(eval_easy2_3) = 1
	Pol(eval_easy2_4) = 1
	Pol(eval_easy2_5) = 1
	Pol(eval_easy2_6) = 1
	Pol(eval_easy2_bb1_in) = 1
	Pol(eval_easy2_bb2_in) = 1
	Pol(eval_easy2_bb3_in) = 0
	Pol(eval_easy2_stop) = -1
	Pol(koat_start) = 1
orients all transitions weakly and the transition
	eval_easy2_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy2_bb3_in(Ar_0, Ar_1)) [ Ar_0 <= 0 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    eval_easy2_start(Ar_0, Ar_1) -> Com_1(eval_easy2_bb0_in(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_bb0_in(Ar_0, Ar_1) -> Com_1(eval_easy2_0(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_0(Ar_0, Ar_1) -> Com_1(eval_easy2_1(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_1(Ar_0, Ar_1) -> Com_1(eval_easy2_2(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_2(Ar_0, Ar_1) -> Com_1(eval_easy2_3(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_3(Ar_0, Ar_1) -> Com_1(eval_easy2_4(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_4(Ar_0, Ar_1) -> Com_1(eval_easy2_5(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_5(Ar_0, Ar_1) -> Com_1(eval_easy2_6(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_6(Ar_0, Ar_1) -> Com_1(eval_easy2_bb1_in(Ar_1, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy2_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy2_bb2_in(Ar_0, Ar_1)) [ Ar_0 > 0 ]
		(Comp: 1, Cost: 1)    eval_easy2_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy2_bb3_in(Ar_0, Ar_1)) [ Ar_0 <= 0 ]
		(Comp: ?, Cost: 1)    eval_easy2_bb2_in(Ar_0, Ar_1) -> Com_1(eval_easy2_bb1_in(Ar_0 - 1, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy2_bb3_in(Ar_0, Ar_1) -> Com_1(eval_easy2_stop(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(eval_easy2_start(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 3 produces the following problem:
4:	T:
		(Comp: 1, Cost: 1)    eval_easy2_start(Ar_0, Ar_1) -> Com_1(eval_easy2_bb0_in(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_bb0_in(Ar_0, Ar_1) -> Com_1(eval_easy2_0(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_0(Ar_0, Ar_1) -> Com_1(eval_easy2_1(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_1(Ar_0, Ar_1) -> Com_1(eval_easy2_2(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_2(Ar_0, Ar_1) -> Com_1(eval_easy2_3(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_3(Ar_0, Ar_1) -> Com_1(eval_easy2_4(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_4(Ar_0, Ar_1) -> Com_1(eval_easy2_5(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_5(Ar_0, Ar_1) -> Com_1(eval_easy2_6(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_6(Ar_0, Ar_1) -> Com_1(eval_easy2_bb1_in(Ar_1, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy2_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy2_bb2_in(Ar_0, Ar_1)) [ Ar_0 > 0 ]
		(Comp: 1, Cost: 1)    eval_easy2_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy2_bb3_in(Ar_0, Ar_1)) [ Ar_0 <= 0 ]
		(Comp: ?, Cost: 1)    eval_easy2_bb2_in(Ar_0, Ar_1) -> Com_1(eval_easy2_bb1_in(Ar_0 - 1, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy2_bb3_in(Ar_0, Ar_1) -> Com_1(eval_easy2_stop(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(eval_easy2_start(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(eval_easy2_start) = 2*V_2 + 2
	Pol(eval_easy2_bb0_in) = 2*V_2 + 2
	Pol(eval_easy2_0) = 2*V_2 + 2
	Pol(eval_easy2_1) = 2*V_2 + 2
	Pol(eval_easy2_2) = 2*V_2 + 2
	Pol(eval_easy2_3) = 2*V_2 + 2
	Pol(eval_easy2_4) = 2*V_2 + 2
	Pol(eval_easy2_5) = 2*V_2 + 2
	Pol(eval_easy2_6) = 2*V_2 + 2
	Pol(eval_easy2_bb1_in) = 2*V_1 + 2
	Pol(eval_easy2_bb2_in) = 2*V_1 + 1
	Pol(eval_easy2_bb3_in) = 2*V_1 + 2
	Pol(eval_easy2_stop) = 2*V_1 + 2
	Pol(koat_start) = 2*V_2 + 2
orients all transitions weakly and the transition
	eval_easy2_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy2_bb2_in(Ar_0, Ar_1)) [ Ar_0 > 0 ]
strictly and produces the following problem:
5:	T:
		(Comp: 1, Cost: 1)             eval_easy2_start(Ar_0, Ar_1) -> Com_1(eval_easy2_bb0_in(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)             eval_easy2_bb0_in(Ar_0, Ar_1) -> Com_1(eval_easy2_0(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)             eval_easy2_0(Ar_0, Ar_1) -> Com_1(eval_easy2_1(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)             eval_easy2_1(Ar_0, Ar_1) -> Com_1(eval_easy2_2(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)             eval_easy2_2(Ar_0, Ar_1) -> Com_1(eval_easy2_3(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)             eval_easy2_3(Ar_0, Ar_1) -> Com_1(eval_easy2_4(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)             eval_easy2_4(Ar_0, Ar_1) -> Com_1(eval_easy2_5(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)             eval_easy2_5(Ar_0, Ar_1) -> Com_1(eval_easy2_6(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)             eval_easy2_6(Ar_0, Ar_1) -> Com_1(eval_easy2_bb1_in(Ar_1, Ar_1))
		(Comp: 2*Ar_1 + 2, Cost: 1)    eval_easy2_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy2_bb2_in(Ar_0, Ar_1)) [ Ar_0 > 0 ]
		(Comp: 1, Cost: 1)             eval_easy2_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy2_bb3_in(Ar_0, Ar_1)) [ Ar_0 <= 0 ]
		(Comp: ?, Cost: 1)             eval_easy2_bb2_in(Ar_0, Ar_1) -> Com_1(eval_easy2_bb1_in(Ar_0 - 1, Ar_1))
		(Comp: 1, Cost: 1)             eval_easy2_bb3_in(Ar_0, Ar_1) -> Com_1(eval_easy2_stop(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)             koat_start(Ar_0, Ar_1) -> Com_1(eval_easy2_start(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 5 produces the following problem:
6:	T:
		(Comp: 1, Cost: 1)             eval_easy2_start(Ar_0, Ar_1) -> Com_1(eval_easy2_bb0_in(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)             eval_easy2_bb0_in(Ar_0, Ar_1) -> Com_1(eval_easy2_0(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)             eval_easy2_0(Ar_0, Ar_1) -> Com_1(eval_easy2_1(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)             eval_easy2_1(Ar_0, Ar_1) -> Com_1(eval_easy2_2(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)             eval_easy2_2(Ar_0, Ar_1) -> Com_1(eval_easy2_3(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)             eval_easy2_3(Ar_0, Ar_1) -> Com_1(eval_easy2_4(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)             eval_easy2_4(Ar_0, Ar_1) -> Com_1(eval_easy2_5(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)             eval_easy2_5(Ar_0, Ar_1) -> Com_1(eval_easy2_6(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)             eval_easy2_6(Ar_0, Ar_1) -> Com_1(eval_easy2_bb1_in(Ar_1, Ar_1))
		(Comp: 2*Ar_1 + 2, Cost: 1)    eval_easy2_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy2_bb2_in(Ar_0, Ar_1)) [ Ar_0 > 0 ]
		(Comp: 1, Cost: 1)             eval_easy2_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy2_bb3_in(Ar_0, Ar_1)) [ Ar_0 <= 0 ]
		(Comp: 2*Ar_1 + 2, Cost: 1)    eval_easy2_bb2_in(Ar_0, Ar_1) -> Com_1(eval_easy2_bb1_in(Ar_0 - 1, Ar_1))
		(Comp: 1, Cost: 1)             eval_easy2_bb3_in(Ar_0, Ar_1) -> Com_1(eval_easy2_stop(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)             koat_start(Ar_0, Ar_1) -> Com_1(eval_easy2_start(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound 4*Ar_1 + 15

Time: 0.592 sec (SMT: 0.572 sec)